AIM (version 1.01)

cv.logistic.interaction: Cross-validation in interaction logistic AIM

Description

Cross-validation for selecting the number of binary rules in the interaction AIM with binary outcomes.

Usage

cv.logistic.interaction(x, trt, y, K.cv=5, num.replicate=1, nsteps, mincut=0.1, backfit=F, maxnumcut=1, dirp=0, weight=1)

Arguments

x

n by p matrix. The covariate matrix

trt

n vector. The treatment indicator

y

n 0/1 vector. The binary response variable

K.cv

K.cv-fold cross validation

num.replicate

number of independent replications of K-fold cross validations.

nsteps

the maximum number of binary rules to be included in the index

mincut

The minimum cutting proportion for the binary rule at either end. It typically is between 0 and 0.2.

backfit

T/F. Whether the existing split points are adjusted after including a new binary rule

maxnumcut

The maximum number of binary splits per predictor

dirp

p vector. The given direction of the binary split for each of the p predictors. 0 represents "no pre-given direction"; 1 represents "(x>cut)"; -1 represents "(x

weight

a positive value. The weight given to responses: "weight=0" means that all observations are equally weighted.

Value

cv.logistic.interaction returns

kmax

the optimal number of binary rules based the cross-validation

meanscore

nsteps-vector. The cross-validated score test statistics (significant at 0.05, if greater than 1.96) for the treatment*index interaction.

pvfit.score

nsteps-vector, the pre-validated score test statistics (significant at 0.05, if greater than 1.96) for the treatment*index interaction.

preval

nsteps by n matrix. Prevalidated fits for individual observation

References

L Tian and R Tibshirani Adaptive index models for marker-based risk stratification, Tech Report, available at http://www-stat.stanford.edu/~tibs/AIM. R Tibshirani and B Efron, Pre-validation and inference in microarrays, Statist. Appl. Genet. Mol. Biol., 1:1-18, 2002.

Details

cv.logistic.interaction implements the K-fold cross-validation for the interaction logistic AIM. It estimates the score test statistics in the test set for testing the treatment*index interaction. It also provides pre-validated fits for each observation and pre-validated score test statistic. The output can be used to select the optimal number of binary rules.

Examples

## generate data
set.seed(1)

n=400
p=10
x=matrix(rnorm(n*p), n, p)
z=(x[,1]<0.2)+(x[,5]>0.2)
trt=rbinom(n,1, 0.5)
beta=1
prb=1/(1+exp(trt-beta*trt*z-0.5))
y=rbinom(n,1,prb)


## cross-validate the logistic interaction AIM 
a=cv.logistic.interaction(x, trt, y, nsteps=10, K.cv=4, num.replicate=5)
 
## examine score test statistics in the test set 
par(mfrow=c(1,2))
plot(a$meanscore, type="l")
plot(a$pvfit.score, type="l")


## construct the index with the optimal number of binary rules 
k.opt=a$kmax
a=logistic.interaction(x, trt, y, nsteps=k.opt)
print(a)